tebert2458,
It is a fairly simple process. Remove the plugs from the new lights, separate the two wires a bit so you can gather one wire from each new light and, using a 'Marr' type connector, connect it to the black wire at the light fixture box. Gather the other leads and connect them to the white lead at the fixture box. Check that there is no bare wire exposed after making the connections.
Check to see if there are any warnings regarding excessive heat from the lights. If the new string of lights are for interior use there should not be a problem.
If you want to purchase a cover plate for the fixture box you should feed the wires through before you connect them to the supply. Ensure that the connector you use is the proper size for the number and size of wires you are joining together. There are large two piece connectors available with a set screw that would probably work best since you can visually inspect the connection before you screw the plastic cover over it.

Good luck, Jim
'Just a handyman trying to help'